Definition of check back
Generally, when we talk about check back, we are talking about a two-player situation after the flop. For check back, you have to be in position, i.e. you speak last on each betting round. Generally, a player goes check back to take his opponent's pulse (a check back is a check after a check, our opponent's). He takes advantage of his position to get as much information as possible about his hand. It is rather rare that a player goes check back a flop with a big hand (although a player may have his reasons to do so).
Reasons for check back
One can check back for many reasons. We can check back to keep the pot small or because our hand is too strong. Or because we are not sure of our opponent's rank. For example, you open in the UTG position with a pair of jacks and a tight player you over-raise (3bet) the small blind. Here, there's no need to do anything but call. The flop falls 2-2-8 and your opponent check out of position. You suspect him of having AA or KK getting ready at check raise all in to make you pay your JJ and QQ. He might also have an AK who missed the flop. You're not sure, so after his check, you decide on check back to get more information about his hand on the turn.